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If the price of a bag of potatoes went up, would you switch to a cheaper brand? That’s the issue at the heart of the debate over how to calculate the Retail Prices Index.

No one said that calculating inflation was easy, but yesterday morning's decision by the Office for National Statistics to stick with the existing method used to calculate Retail Prices Index provides an intriguing insight into the complexities of choosing exactly which mathematical model is best for measuring price rises.

The maths can be mindbogglingly complicated, but it all boils down to the price of a bag of potatoes, says Andrew McCulloch, writing in the Royal Statistical Society's magazine Significance.

McCulloch sets out the scenario of a potato index that consists of a bag of Golden Wonder potatoes and a bag of Maris Piper potatoes, both costing £1. Imagine that the price of the Golden Wonder potatoes rose to £2, then what’s the average price rise of potatoes?

The Retail Prices Index uses a simple "arithmetic mean" to calculate price increases: in this case the price of the two products divided by two, giving an average price of £1.50, a 50% rise in prices, according to the RPI.

Which all sounds logical enough, until you take into account how we actually react to rising prices.

In the case of our potato index, many of us would simply switch to cheaper varieties, economists say.

So assume that instead of simply reacting to the price rise by spending £1 on a bag of Maris Piper and £2 on a bag of Golden Wonder – a total of £3 – we split the budget in two. Half (£1.50) goes on Maris Piper potatoes, buying us a whopping 1.415kg and the other half and the other 50% on Golden Wonder (0.707 of a bag).

Our £3 now buys us 2.25 bags of potatoes, which McCulloch calculates means we only need an extra 41% income to pay for our potatoes, a markedly lower figure for inflation than suggested by the RPI.

That, broadly speaking, is the difference between the much-criticised RPI , and the more sophisticated Consumer Prices Index, which uses something more akin to a weighted average, called a "geometric mean", that takes into account how our purchasing power is affected by price rises.

The maths are complicated – the geometric mean is defined as the “the nth root of n numbers” (in the case of our potatoes the square root of two prices multiplied together = the square root of 1 x 2, which in our case is £1.41 and equivalent to a 41% rise in potato prices) – but the average price rises are generally lower using the CPI approach.

Intriguingly, while opting to keep the existing RPI as one of its measures of inflation, the ONS is introducing a third measure of inflation called the Retail Prices Index "J", or RPI-J, that uses a similar method for calculating the mean price rise as the CPI.

It is still unclear exactly how this new measure of RPI will be used, but it all goes to prove that when it comes to price rises and measuring inflation, it's all about as clear as mud. Or should that be spud?